Arbitrage vs value betting.

One wrong price, two uses

A tennis match is close to even. A sharp bookmaker, one with low margins and a lot of informed money, prices it at 1.95 on each player. A slower bookmaker still shows 2.10 on the first player. That 2.10 is too high, and there are two things you can do with it.

Arbitrage: back the first player at 2.10, and back the second player somewhere else at the best price you can find, say 2.05. Whoever wins, you are paid.

Value betting: back the first player at 2.10 and stop there. You have a bet at better odds than the true chance justifies. It will lose about half the time.

The arb: cover everything

With 1,000 split between 2.10 and 2.05 the return is about 1,037 on either result, a profit of 3.7% of the total. The sums are in How to calculate an arb, and the calculator does them for you.

The second bet is insurance, and insurance has a price. The other side was not mispriced; you backed it at ordinary odds, margin included, to remove the uncertainty. That is why an arb pays less than the mispricing behind it.

The value bet: take only the good price

A value bet needs an estimate of the true chance. The usual source is a sharp bookmaker's price with its margin removed. At 1.95 and 1.95 the margin is about 2.6%; take it out and each player is a 50% chance, or fair odds of 2.00.

The expected value of a bet is what it would pay on average if you could place it many times:

Stake 100. Half the time you win 110, half the time you lose 100, and the average is +5. On a single bet that average means nothing: you are up 110 or down 100. It only shows in the long run, and the long run is longer than most people expect.

What the swings look like

Take 500 value bets of 100 each, all at 2.10 on a true 50% chance. The expected profit is 2,500. The figure shows one simulated run of those bets next to 500 arbs of the same size at 2%.

Some arithmetic on the same bet, placed at a flat 100 with a genuine 5% edge:

• After 100 bets the expected profit is 500, and the chance of being behind is about three in ten.
• After 1,000 bets the expected profit is 5,000, and the chance of being behind is still about one in fifteen.
• A run of eight losses in a row turns up somewhere in 1,000 such bets about 86% of the time.

All of that assumes the edge is real. If your estimate of the true chance is off by a few points, the 5% can be nothing at all, and it takes hundreds of bets to find out.

Side by side

Where each one fails

Arbitrage

• Half an arb. The first bet is on and the second price has gone. You now hold a single bet you did not choose.
• A void. One bookmaker cancels its side as a pricing error. The other side stands.
• Different rules. Two bookmakers settle the same event differently, and both of your bets lose, or one is refunded.
• Low limits. The mispriced side takes 30, and 3% of 30 is not worth the evening.

Value betting

• A wrong estimate. The "sharp" price was stale too, or the market was thin, and the edge was never there.
• Variance. Everything in the section above. It is not a malfunction, and it still empties bankrolls that stake too much per bet.
• You. Doubling stakes after a bad run, or stopping after one, turns a positive expectation into a negative result.
• A void, again. A very large "value" is as likely to be a pricing error as a large arb is, and is cancelled the same way.

Staking matters far more in value betting. Flat stakes of 1 to 2% of the bankroll, or a fraction of the Kelly stake, are the usual defences. In arbing a bad stake costs a little profit. In value betting it costs the bankroll.

Which suits you

Arbing fits if you want each day to end roughly where the arithmetic said it would, you have the time to place two bets quickly, and you are willing to keep balances at many bookmakers. Its ceiling is set by limits and by how fast your money comes back.

Value betting fits if you can watch a bankroll fall for three weeks and place the next bet at the same stake, without checking whether the method "still works". It needs fewer accounts and less speed, and more patience than most people have.

Many bettors end up doing both. They are closer than they look: an arb whose second leg disappeared is a value bet, provided the leg you did place was the mispriced one. And when a bookmaker's limit is too low to make an arb worthwhile, the mispriced side alone can still be a sensible bet. Keep the bookmakers' reaction in mind either way; it is covered in the guide to limits.

In ArbStrike

The scanner lists both, separately. Pre-match arbs come with the stake for each side worked out and a note on which bet to place first. Value bets are single prices that stand above a sharp bookmaker's fair odds, shown with the expected value of each.

The smaller pre-match arbs are free. Pro, at $49 a month, opens all of them. Elite, at $99, adds arbs on games in play and the value bets. Pricing has the details. New to all of this? Start with What is arbitrage betting?